When designing, for example, a submarine or an airplane, it is necessary to predict the physical properties of the fluid around the object. The distribution of the physical properties (pressure, velocity, temperature, etc.) may be obtained by solving the governing equations such as the Navier-Stokes equations. However, since it is very difficult, approximated solutions are obtained by, for example, using the finite element method.
However, since this method is based on the continuum hypothesis, it cannot provide right solutions for rarefied gas or fluids flowing around micro- or nano-sized objects.
Furthermore, the conventional methods do not provide accurate predictions about dynamics of complex fluid systems, bubbles or droplets, wetting on solid surfaces, interfacial slip, fluid flow through porous materials, fluid flow through blood vessels, and so forth.
Molecular dynamics, wherein a fluid is not viewed as a continuum but as a set of particles constituting it and equations of motion are solved for the individual particles in the molecular level, may be employed to solve the problem. But, it is very inefficient. One of the methods presented to solve this problem is the lattice Boltzmann method.
In this scheme, the solution may be obtained by a discretization or discrete process of the Boltzmann equation and the Bhatnagar-Gross-Krook (BGK) collision term. However, use of the lattice Boltzmann method has been used mainly restricted for isothermal fluids. Although the thermal lattice Boltzmann method has been proposed to treat nonisothermal i.e. thermal fluids, it has many problems associated with stability, accuracy, and efficiency.
The modifier “thermal” in the thermal lattice Boltzmann method is given to denote that the method is applicable to thermal fluids as well as isothermal fluids, whereas the early lattice Boltzmann methods are applicable only to isothermal fluids.